I haven't done the math, but I suspect there are plenty of solutions like this, you'll just have to calculate them.
Given the restriction that you can only guess "words", you need to improve the wordlist anyway. I had "denty" rejected as a guess, which was not a good look when "folky" turned out to be an official answer.
My other suggestion would be to revise the keyboard input - it's much easier to type the entire word I want to guess than to look at which letters are missing and only type those.
And while it's not a suggestion, I would note that your "cruelly challenging" difficulty level is noticeably easier than the levels that are supposed to be below it, because it provides no clues. This makes it much easier to determine which letters go in which word.